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    <p>Fixed-precision floating point types, the ones natively supported by your CPU's floating point unit (<code>float</code>, <code>double</code>, <code>real</code>) are not optimal for any calculation that needs many digits of precision, such as the example you've given.</p> <p>The problem is that these floating-point types have a finite number of digits of precision (binary digits, actually) that limits the length of number that can be represented by such a data type. The <code>float</code> type has a limit of approximately 7 decimal digits (e.g. 3.141593); the <code>double</code> type is limited to 14 (e.g. 3.1415926535898); and the <code>real</code> type has a similar limit (slightly more than that of <code>double</code>).</p> <p>Adding exceedingly small numbers to a floating-point value will therefore result in those digits being lost. Watch what happens when we add the following two float values together:</p> <pre><code>float a = 1.234567f, b = 0.0000000001234567 float c = a + b; writefln("a = %f b = %f c = %f", a, b, c); </code></pre> <p>Both <code>a</code> and <code>b</code> are valid float values and retain approximately 7 digits of precision apiece in isolation. But when added, only the frontmost 7 digits are preserved because it's getting shoved back into a float:</p> <pre><code>1.2345670001234567 =&gt; 1.234567|0001234567 =&gt; 1.234567 ^^^^^^^^^^^ sent to the bit bucket </code></pre> <p>So <code>c</code> ends up equal to <code>a</code> because the finer digits of precision from the addition of <code>a</code> and <code>b</code> get whacked off.</p> <p><a href="https://stackoverflow.com/questions/1218149">Here's another explanation of the concept</a>, probably much better than mine.</p> <hr> <p>The answer to this problem is arbitrary-precision arithmetic. Unfortunately, support for arbitrary-precision arithmetic is not in CPU hardware; therefore, it's not (typically) in your programming language. However, there are many libraries that support arbitrary-precision floating-point types and the math you want to perform on them. See <a href="https://stackoverflow.com/questions/2568446">this question</a> for some suggestions. You probably won't find any D-specific libraries for this purpose today, but there are plenty of C libraries (GMP, MPFR, and so on) that should be easy enough to use in isolation, and even more so if you can find D bindings for one of them.</p>
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